The vector field F(x, y) = (y, y + 7) represents a vector at each point in the xy-plane. To match this vector field with the correct plot, we need to understand how the vector components vary across the plane.
In this case, the x-component of the vector is always 0, while the y-component varies. Specifically, the y-component is equal to the y-coordinate plus 7.
Let's consider a few points to better understand this vector field:
1. At the point (0, 0), the vector F is (0, 7). This means that the vector starts at the origin and points vertically upward with a magnitude of 7.
2. At the point (1, 1), the vector F is (1, 8). This vector points diagonally upwards and to the right from the point (1, 1).
3. At the point (-1, -1), the vector F is (-1, 6). This vector points diagonally downwards and to the left from the point (-1, -1).
From these examples, we can see that the vectors in this field are parallel and have a constant magnitude of 7. The direction of the vectors depends on the location in the xy-plane.
To summarize, the vector field F(x, y) = (y, y + 7) represents a set of vectors with a constant magnitude of 7. The vectors are parallel and point in various directions depending on the location in the xy-plane.